On a Theorem of J. Ossowski

Consider any matrix of zeros and ones with at mostnones in each row and fewer than (k+1) nones in all. Ossowski showed that, by deleting no more thankcolumns, one can get a matrix which contains nor×(n−r+1) submatrix of ones forr=1, 2, …, n. We give a short proof of Ossowskiʹs theorem in the slightly stronger form: any minimal set of columns, whose deletion has the desired effect, has cardinality at mostk.